A method to determine coating’s Young’s modulus from frequency shift of silicon cantilevers Riccardo DeSalvo, Innocenzo Pinto Wave group, University of Sannio at Benevento, Italy Shiuh Chao, Jeng-shiun Ou, Vincent Huang, Julie Wang, Steve Wang, Howard Pan, Chia-Wei Lee National Tsing Hua University, Taiwan Roma-9/10/12JGW-G (LIGO-G )1

The physical effect Adding a coating makes a cantilever stiffer Resonant frequency moves up in frequency Comparing the frequency shift measured with a Finite Element Model one can allow us to extract the coating Young’s modulus Roma-9/10/12JGW-G (LIGO-G )2

The enabler Thick holding pad reduces re-clamping error and produce high measurement precision mm 10 mm 92 μm or 52 μm 34 mm 0.35mm 500 μm 5.5mm Roma-9/10/12JGW-G (LIGO-G )3

Frequency of silicon cantilever substrate And with 3 nano-layers coated Frequency of silicon cantilever substrate And with 19 nano-layers coated f 0 = (Hz) τ =635.0(sec) Q= πf 0 τ φ=4.55x10 -6 f 0 = (Hz) τ = 501.5(sec) Q= πf 0 τ φ=5.82x10 -6 f 0 = (Hz) τ =731.4(sec) Q= πf 0 τ φ=4.49x10 -6 f 0 = (Hz) τ =551.5(sec) Q= πf 0 τ φ=5.32x10 -6 Roma-9/10/12JGW-G (LIGO-G )4

Can measure the frequency shift caused by coating with precision < Thermal frequency shifts likely dominate MUST measure temperature to measure thermal shift Roma-9/10/12JGW-G (LIGO-G )5

Thermal effects ∂Y/∂T = 127 x / o C Thermal shift∂f/∂T ~ / o C Measured ∆f ~ Temperature affects the result Roma-9/10/12JGW-G (LIGO-G )6

Question 1 Will the sensitivity be enough? Frequency measurements at 10 -6, OK Simultaneous measurements over several higher mode resonant frequencies will increase the sensitivity Roma-9/10/12JGW-G (LIGO-G )7

Question 2 Is this the desired Young’s Modulus? This measurement extracts the parallel Young’s Modulus Coating thermal noise requires the perpendicular Young’s Modulus Roma-9/10/12JGW-G (LIGO-G )8

How to measure the // Young’s Modulus Konrad Samwer uses a modified Atomic Force Acoustic Microscope to measure the local elasticity with a no-indentation method The atomic force microscope needle is brought in contact, in the elastic regime From the variation of resonant frequency of the needle’s cantilever the local Young’s modulus of the material is measured Roma-9/10/12JGW-G (LIGO-G )9 Local elastic properties of a metallic glass Hannes Wagner, Dennis Bedorf, Stefan Küchemann, Moritz Schwabe, Bo Zhang, Walter Arnold & Konrad Samwer Nature Materials 10, 439–442 (2011) And supplemental material

Typical AFAM scan a, Map of the local contact-resonance frequencies on amorphous glass. b, on crystal. Both maps represent the results of AFAM data at 100 different positions on the samples surfaces Roma-9/10/12JGW-G (LIGO-G )10

Good and bad Samwer’s technique only measures Young’s modulus over the first nanometer depth A mixture of parallel and perpendicular Young’s modulus is measured The perpendicular Young’s modulus can be disentangled with the cantilever frequency shift information Roma-9/10/12JGW-G (LIGO-G )11